Testing Hall-Post inequalities with exactly solvable N-body problems

The Hall-Post inequalities provide lower bounds on N-body energies in terms of N ' -body energies with N' < N. They are rewritten and generalized to b e tested with exactly solvable models of Calogero-Sutherland type in one an d higher dimensions. The bound for N spinless fermions in one dimension is better saturated at large coupling than for noninteracting fermions in an o scillator potential.